Open AccessFORCED OSCILLATIONS OF NONLINEAR HYPERBOLIC EQUATIONS WITH FUNCTIONAL ARGUMENTS
Author(s) -
Wei-Nian Li,
Baotong Cui
Publication year - 1999
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.30.1999.4212
Subject(s) - mathematics , domain (mathematical analysis) , omega , bounded function , boundary (topology) , laplace operator , piecewise , space (punctuation) , combinatorics , hyperbolic space , euclidean space , mathematical analysis , nonlinear system , mathematical physics , pure mathematics , physics , quantum mechanics , linguistics , philosophy
In this paper, sufficient conditions for the forced oscillations of hyperbolic equations with functional arguments of the form \[\frac{\partial^2}{\partial t^2}=a(t)\Delta u(x, t)+\sum_{i=1}^m a_i(t)\Delta u(x, \rho(t))-\sum_{j=1}^k q_j(x, t)f_j(u(x, \sigma_j(t)))+f(x, t) \]$(x, t)\in\Omega\times[0, \infty)$ are obtained, where $\Omega$ is a bounded domain in $\mathbb{R}^n$ with piecewise smooth boundary $\partial\Omega$ and $\Delta$ is the Laplacian in Euclidean $n$-space $\mathbb{R}^n$.